AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

Computer simulation of diffusion processes in tilt spatio-periodic potentials

Нещодавно було показано, що в істотно нерівноважних системах коефіцієнт дифузії може вести себе немонотонно з температурою. Одним із прикладів таких систем з аномальною температурної залежністю є рух броунівських часток в просторово-періодичних структурах. Метою статті було дослідження зміни температурної залежності дифузії в недодемпфованих системах з низьким коефіцієнтом тертя. В роботі методами комп'ютерного моделювання вивчено зміна коефіцієнта дифузії частинок в широкому діапазоні температур в нахилених просторово-періодичних потенціалах для різних значень коефіцієнта тертя. Показано, що дифузія досягає максимуму при певній величині зовнішньої сили. Її значення залежить від величини коефіцієнта тертя. Показано, що на відміну від звичайної залежності Аррениуса, в разі нахиленого періодичного потенціалу, максимальний коефіцієнт дифузії зростає, а не зменшується з пониженням температури експоненціальним чином. Встановлено, що така залежність характерна для всіх недодемпфованих систем. Показано, що для просторово-періодичних структур існує обмежена ділянка сил, в якому спостерігається зростання коефіцієнта дифузії зі зменшенням температури. Це область так званої температурно-аномальної дифузії (ТАД). Визначено ширина і положення області ТАД в залежності від коефіцієнта тертя γ і параметрів системи. Показано, що зі зменшенням γ, ширина області ТАД зменшується пропорційно γ. При цьому коефіцієнт дифузії в області ТАД, навпаки зростає ~γ. Отримані дані про температурно-аномальної дифузії мають важливе значення для різних областей фізики і техніки та відкривають перспективи створення новітніх технологій управління процесами дифузії.It was recently shown that in essentially nonequilibrium systems, the diffusion coefficient can behave nonmonotonically with temperature. One example of such systems with anomalous temperature dependence is the motion of Brownian particles in spatially periodic structures. The aim of the article was to study the change in the temperature dependence of diffusion in underdamped systems with a low coefficient of friction. In this paper, computer simulation methods are used to study the change in the diffusion coefficient of particles in a wide range of temperatures in oblique spatially periodic potentials for different values of the friction coefficient. It is shown that diffusion reaches a maximum at a certain external force. Its value depends on the coefficient of friction. It is shown that, in contrast to the usual Arrhenius dependence, in the case of an inclined periodic potential, the maximum diffusion coefficient increases while temperature is decreasing exponentially. It is established that such a dependence is common to all underdamped systems. It is shown that for spatially periodic structures there is a limited portion of forces in which an increase in the diffusion coefficient while decreasing temperature is observed. This is the area of the so-called temperature-anomalous diffusion (TAD). The width and position of the TAD region are determined depending on the friction coefficient γ and the system parameters. It has been shown that a decrease in γ, width TAD region decreases proportionally γ. In this case, the diffusion coefficient in the TAD region, on the contrary, increases ~γ. The data obtained on the temperature and the anomalous diffusion are important for various fields of physics and engineering, and opens new prospects for a diffusion process control technology

Dynamics of Bacillus thuringiensis var. israelensis and Lysinibacillus sphaericus spores in urban catch basins after simultaneous application against mosquito larvae

Bacillus thuringiensis var. israelensis (Bti) and Lysinibacillus sphaericus (Lsph) are extensively used in mosquito control programs. These biocides are the active ingredients of a commercial larvicide. Quantitative data on the fate of both Bti and Lsph applied together for the control of mosquitoes in urban drainage structures such as catch basins are lacking. We evaluated the dynamics and persistence of Bti and Lsph spores released through their concomitant application in urban catch basins in southern Switzerland. Detection and quantification of spores over time in water and sludge samples from catch basins were carried out using quantitative real-time PCR targeting both cry4A and cry4B toxin genes for Bti and the binA gene for Lsph. After treatment, Bti and Lsph spores attained concentrations of 3.76 (± 0.08) and 4.13 (± 0.09) log ml(-1) in water, then decreased progressively over time, reaching baseline values. For both Bti and Lsph, spore levels in the order of 10(5) g(-1) were observed in the bottom sludge two days after the treatment and remained constant for the whole test period (275 days). Indigenous Lsph strains were isolated from previously untreated catch basins. A selection of those was genotyped using pulsed field gel electrophoresis of SmaI-digested chromosomal DNA, revealing that a subset of isolates were members of the clonal population of strain 2362. No safety issues related to the use of this biopesticide in the environment have been observed during this study, because no significant increase in the number of spores was seen during the long observation period. The isolation of native Lysinibacillus sphaericus strains belonging to the same clonal population as strain 2362 from catch basins never treated with Lsph-based products indicates that the use of a combination of Bti and Lsph for the control of mosquitoes does not introduce non-indigenous microorganisms in this area

Refractoriness of hepatitis C virus internal ribosome entry site to processing by Dicer in vivo

<p>Abstract</p> <p>Background</p> <p>Hepatitis C virus (HCV) is a positive-strand RNA virus harboring a highly structured internal ribosome entry site (IRES) in the 5' nontranslated region of its genome. Important for initiating translation of viral RNAs into proteins, the HCV IRES is composed of RNA structures reminiscent of microRNA precursors that may be targeted by the host RNA silencing machinery.</p> <p>Results</p> <p>We report that HCV IRES can be recognized and processed into small RNAs by the human ribonuclease Dicer in vitro. Furthermore, we identify domains II, III and VI of HCV IRES as potential substrates for Dicer in vitro. However, maintenance of the functional integrity of the HCV IRES in response to Dicer overexpression suggests that the structure of the HCV IRES abrogates its processing by Dicer in vivo.</p> <p>Conclusion</p> <p>Our results suggest that the HCV IRES may have evolved to adopt a structure or a cellular context that is refractory to Dicer processing, which may contribute to viral escape of the host RNA silencing machinery.</p

Predictive labeling

Abstract. Semantic labeling is a transformation technique for proving the termination of rewrite systems. The semantic part is given by a quasi-model of the rewrite rules. In this paper we present a variant of semantic labeling in which the quasi-model condition is only demanded for the usable rules induced by the labeling. Our variant is less powerful in theory but maybe more useful in practice.

Orderings for innermost termination

This paper shows that the suitable orderings for proving innermost termination are characterized by the innermost parallel monotonicity, IP-monotonicity for short. This property may lead to several innermost-specific orderings. Here, an IP-monotonic version of the Recursive Path Ordering is presented. This variant can be used (directly or as ingredient of the Dependency Pairs method) for proving innermost termination of non-terminating term rewrite systems